Problem: A few families took a trip to an amusement park together. Tickets cost $$8.50$ each for adults and $$3.00$ each for kids, and the group paid $$61.00$ in total. There were $5$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8.5x+3y = 61}$ ${x = y-5}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-5}$ for $x$ in the first equation. ${8.5}{(y-5)}{+ 3y = 61}$ Simplify and solve for $y$ $ 8.5y-42.5 + 3y = 61 $ $ 11.5y-42.5 = 61 $ $ 11.5y = 103.5 $ $ y = \dfrac{103.5}{11.5} $ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into ${x = y-5}$ to find $x$ ${x = }{(9)}{ - 5}$ ${x = 4}$ You can also plug ${y = 9}$ into ${8.5x+3y = 61}$ and get the same answer for $x$ ${8.5x + 3}{(9)}{= 61}$ ${x = 4}$ There were $4$ adults and $9$ kids.